A photo shows the couple who killed 14 people in California on December 3, 2015. [Photo: Xinhua]

The Islamic State militant group has claimed on its online radio station that the married couple who killed 14 people in California earlier this week were followers of the militant group.

"We begin in California where two soldiers of the Khilafah executed and attacked on the inland regional center in San Bernardino, California, on the 20th of Safar."

The declaration comes three days after U.S.-born Syed Rizwan Farook and his spouse, Tashfeen Malik carried out the attack on a holiday party for civil servants in San Bernardino, about 100 kilometers east of Los Angeles.

The two died hours later in a shootout with police on Wednesday.

The FBI is investigating the attack as an "act of terrorism."

U.S. Government sources have said Malik and her husband may have been inspired by Islamic State, but as yet there was no evidence the attack had been directed by the militant group or that the organization even knew who they were.

If the mass shooting proves to have been the work of people inspired by Islamist militants, it would mark the deadliest such attack in the United States since September 11, 2001.